What is the domain of f(x)=(x^2+3x-10)/(2x^2+9x-5) ?

The domain of f(x)=(x^2+3x-10)/(2x^2+9x-5) is x 1/2

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domain of f(x)=(x^2+3x-10)/(2x^2+9x-5)

domain

x < - 5 or - 5 < x < \frac{1}{2} or x > \frac{1}{2}

Interval Notation

(- \infty, - 5) \cup (- 5, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{1}{2}, x = - 5

The function domain

x < - 5 or - 5 < x < \frac{1}{2} or x > \frac{1}{2}

What is the domain of f(x)=(x^2+3x-10)/(2x^2+9x-5) ?
The domain of f(x)=(x^2+3x-10)/(2x^2+9x-5) is x<-5\lor-5<x< 1/2 \lor x> 1/2